Question

Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measure the angle between the chord and the radius. What can you conclude about the intersection of a chord and the radius that bisects it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part B
Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii
OA and OC
Part C
In this part of the activity, you will investigate the converse of the theorem stated in part A. To get started, reopen GeoGebra.

Draw a circle of any radius, and draw a chord on it. Construct the radius of the circle that is perpendicular to the chord. Measure the line segments into which the radius divides the chords. How are the line segments related? What can you conclude about the intersection of a chord and a radius that is perpendicular to it? Take a screenshot of your construction, save it, and insert the image below your answer.

Part D
Write a paragraph proof of your conclusion in part C. To begin your proof, draw radii
OA and OC

Answer 1

Answer:

Part A: See the image attached. The angle between the radius and the chord will always be 90 degree if the radius is perpendicular to the chord

Part B: There are many ways to prove this and here is mine

Prove OC is perpendicular to AB

We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)

to prove this that they apply to the SSS criteria:

m∠ADO=m∠BDO

m∠ADO=90°=m∠BDO

Part C: See the image attached. A radius is perpendicular to a chord when the chord is equally divided in half by the radius.

Part D: There are many ways to prove this and here is mine

Prove OC is perpendicular to AB

AO=BO because AO and BO are both radii

OD≅OD by reflexive theorem

ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side

AB≅BC means that OC is perpendicular to AB

If you are still confused then I recommend watching these vdos by khan academy about proving perpendicular radius bisector: https://youtu.be/2NgzruZ4_5c

https://youtu.be/TgDk06Qayxw

Hope this helped bye:)